Techniques for estimating expected performance in a task assignment system

ABSTRACT

Techniques for estimating expected performance of a task assignment strategy in a task assignment system are disclosed. In one particular embodiment, the techniques may be realized as a method comprising receiving, by at least one computer processor communicatively coupled to a task assignment system, a plurality of historical agent task assignments; determining, by the at least one computer processor, a sample of the plurality based on a strategy for pairing agents with tasks; determining, by the at least one computer processor, an expected performance of the strategy based on the sample; outputting, by the at least one computer processor, the expected performance; and optimizing, by the at least one computer processor, the performance of the task assignment system based on the expected performance.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a continuation of U.S. patent application Ser. No.16/173,997, filed Oct. 29, 2018, now U.S. Pat. No. 10,375,246, which isa continuation of U.S. patent application Ser. No. 15/648,788, filedJul. 13, 2017, now U.S. Pat. No. 10,116,795, which is a continuation ofU.S. patent application Ser. No. 15/645,277, filed Jul. 10, 2017, nowU.S. Pat. No. 10,122,860, which are hereby incorporated by reference intheir entirety as if fully set forth herein.

FIELD OF THE DISCLOSURE

This disclosure generally relates to performance in a task assignmentsystem, and, more particularly, to techniques for estimating expectedperformance of task assignment strategies in a task assignment system.

BACKGROUND OF THE DISCLOSURE

A typical task assignment system assigns a finite number of tasks to afinite number of workers (“agents”) over a period of time. One exampleof a task assignment system is a contact center (e.g., a call center).In a call center, a finite number of agents are available during a givenshift or other period of time, and a finite number of callers call intothe call center during the shift. Each caller, with various needs andreasons for calling, represents a task assigned to one of the callcenter agents.

A typical task assignment strategy determines which tasks are assignedto which agents. Typically, a task assignment strategy is derived frominsights that certain types of agents perform better with certain typesof tasks, and these agents are assigned specific tasks based on theseinsights. In the example of a call center, the insight may be thatagents skilled at sales should be preferentially assigned to salesqueues of callers seeking to make a purchase, while agents skilled attechnical support should be preferentially assigned to technical supportqueues of callers seeking a solution to a technical problem.

Although typical task assignment strategies may be effective atimproving the performance of typical task assignment systems in someinstances, in other instances they may have no substantial impact onperformance at best or degrade performance at worst. Typically,instances under which typical task assignment strategies may beineffective are those that do not account for the comparative advantageof agents assigned to different types of tasks.

In view of the foregoing, it may be understood that there may be a needfor a system that enables estimation of the expected performance ofdifferent task assignment strategies for the assignment of a finitenumber of tasks to a finite number of agents over a period of time in atask assignment system.

SUMMARY OF THE DISCLOSURE

Techniques for estimating expected performance of a task assignmentstrategy in a task assignment system are disclosed. In one particularembodiment, the techniques may be realized as a method comprisingreceiving, by at least one computer processor communicatively coupled toa task assignment system, a plurality of historical agent taskassignments; determining, by the at least one computer processor, asample of the plurality based on a strategy for pairing agents withtasks; determining, by the at least one computer processor, an expectedperformance of the strategy based on the sample; outputting, by the atleast one computer processor, the expected performance; and optimizing,by the at least one computer processor, the performance of the taskassignment system based on the expected performance.

In accordance with other aspects of this particular embodiment, the taskassignment system may be a contact center, and wherein the strategy mayassign contacts to contact center agents. In accordance with otheraspects of this particular embodiment, the method may further compriseoversampling, by the at least one computer processor, the plurality ofhistorical agent task assignments by determining a plurality of samplescomprising at least one overlapping historical agent task assignment ofthe plurality of historical agent task assignments.

In accordance with other aspects of this particular embodiment, themethod may further comprise determining, by the at least one computerprocessor, a bias in the sample; and accounting, by the at least onecomputer processor, for the bias in the expected performance.

In accordance with other aspects of this particular embodiment, the biasmay be attributable to an overrepresentation of a subset of agents inthe sample or an overrepresentation of a subset of task types in thesample.

In accordance with other aspects of this particular embodiment,determining the expected performance may comprise determining, by the atleast one computer processor, a plurality of samples of the plurality ofhistorical agent task assignments.

In accordance with other aspects of this particular embodiment, themethod may further comprise partitioning, by the at least one computerprocessor, the plurality of historical agent task assignments into afirst subset of historical agent task assignments and a holdout subsetof historical agent task assignments different from the first subset;and generating, by the at least one computer processor, the strategybased on the first subset, wherein the sample is a subset of the holdoutsubset, and wherein determining the expected performance is based on theholdout subset.

In accordance with other aspects of this particular embodiment, themethod may further comprise over-representing in the holdout subsethistorical agent task assignments attributable to a second strategy forpairing agents with tasks different from the strategy.

In accordance with other aspects of this particular embodiment,determining the expected performance may be based on a plurality ofholdout subsets.

In accordance with other aspects of this particular embodiment, themethod may further comprise determining a standard error associated withthe expected performance based on the plurality of holdout subsets.

In accordance with other aspects of this particular embodiment, thesample may be associated with an amount of performance differencebetween expected performance of the sample and peak performance of thestrategy.

In another particular embodiment, the techniques may be realized as asystem comprising at least one computer processor communicativelycoupled to a task assignment system, wherein the at least one computerprocessor is configured to perform the steps in the above-discussedmethod.

In another particular embodiment, the techniques may be realized as anarticle of manufacture comprising a non-transitory processor readablemedium and instructions stored on the medium, wherein the instructionsare configured to be readable from the medium by at least one computerprocessor communicatively coupled to a task assignment system andthereby cause the at least one computer processor to operate to performthe steps in the above-discussed method.

In another particular embodiment, the techniques may be realized as amethod comprising: receiving, by at least one computer processorcommunicatively coupled to a task assignment system, a plurality ofhistorical agent task assignments; determining, by the at least onecomputer processor, a weighting of at least one of the plurality basedon a strategy for pairing agents with tasks; determining, by the atleast one computer processor, an expected performance of the strategybased on the weighting; and outputting, by the at least one computerprocessor, the expected performance, wherein the expected performance ofthe strategy demonstrates that performance of a task assignment systemmay be optimized if the task assignment system is configured to use thestrategy.

In accordance with other aspects of this particular embodiment, the taskassignment system may be a contact center, and wherein the strategyassigns contacts to contact center agents.

In accordance with other aspects of this particular embodiment, at leastone weighting may be zero or epsilon.

In accordance with other aspects of this particular embodiment, themethod may further comprise determining, by the at least one computerprocessor, a bias in the sample; and accounting, by the at least onecomputer processor, for the bias in the expected performance.

In accordance with other aspects of this particular embodiment, the biasmay be attributable to an overweighting of a subset of agents or anoverweighting of a subset of task types.

In accordance with other aspects of this particular embodiment,determining the expected performance comprises combining at least twoweighted outcomes corresponding to at least two weighted pairings in thesample.

In another particular embodiment, the techniques may be realized as asystem comprising at least one computer processor communicativelycoupled to a task assignment system, wherein the at least one computerprocessor is configured to perform the steps in the above-discussedmethod.

In another particular embodiment, the techniques may be realized as anarticle of manufacture comprising a non-transitory processor readablemedium and instructions stored on the medium, wherein the instructionsare configured to be readable from the medium by at least one computerprocessor communicatively coupled to a task assignment system andthereby cause the at least one computer processor to operate to performthe steps in the above-discussed method.

The present disclosure will now be described in more detail withreference to particular embodiments thereof as shown in the accompanyingdrawings. While the present disclosure is described below with referenceto particular embodiments, it should be understood that the presentdisclosure is not limited thereto. Those of ordinary skill in the arthaving access to the teachings herein will recognize additionalimplementations, modifications, and embodiments, as well as other fieldsof use, which are within the scope of the present disclosure asdescribed herein, and with respect to which the present disclosure maybe of significant utility.

BRIEF DESCRIPTION OF THE DRAWINGS

To facilitate a fuller understanding of the present disclosure,reference is now made to the accompanying drawings, in which likeelements are referenced with like numerals. These drawings should not beconstrued as limiting the present disclosure, but are intended to beillustrative only.

FIG. 1 shows a block diagram of a task assignment system according toembodiments of the present disclosure.

FIG. 2 shows a block diagram of a contact center according toembodiments of the present disclosure.

FIG. 3A depicts a schematic representation of a task assignment modelaccording to embodiments of the present disclosure.

FIG. 3B depicts a schematic representation of a contact pairing modelaccording to embodiments of the present disclosure.

FIG. 4A shows a schematic representation of a task assignment strategyexpected performance estimation according to embodiments of the presentdisclosure.

FIG. 4B shows a schematic representation of a task assignment strategyexpected performance estimation according to embodiments of the presentdisclosure.

FIG. 4C shows a schematic representation of a task assignment strategyexpected performance estimation according to embodiments of the presentdisclosure.

FIG. 4D shows a schematic representation of a task assignment strategyexpected performance estimation according to embodiments of the presentdisclosure.

FIG. 4E shows a schematic representation of a task assignment strategyexpected performance estimation according to embodiments of the presentdisclosure.

FIG. 4F shows a schematic representation of a task assignment strategyexpected performance estimation according to embodiments of the presentdisclosure.

FIG. 4G shows a schematic representation of a task assignment strategyexpected performance estimation according to embodiments of the presentdisclosure.

FIG. 4H shows a schematic representation of a task assignment strategyexpected performance estimation according to embodiments of the presentdisclosure.

FIG. 4I shows a schematic representation of a task assignment strategyexpected performance estimation according to embodiments of the presentdisclosure.

FIG. 4J shows a schematic representation of a task assignment strategyexpected performance estimation according to embodiments of the presentdisclosure.

FIG. 4K shows a schematic representation of a task assignment strategyexpected performance estimation according to embodiments of the presentdisclosure.

FIG. 5 shows a schematic representation of a task assignment payoutmatrix according to embodiments of the present disclosure.

FIG. 6A shows a flow diagram of an expected performance estimationmethod according to embodiments of the present disclosure.

FIG. 6B shows a flow diagram of an expected performance estimationmethod according to embodiments of the present disclosure.

FIG. 7 depicts a flow diagram of an expected performance estimationmethod according to embodiments of the present disclosure.

FIG. 8 depicts a flow diagram of an expected performance estimationmethod according to embodiments of the present disclosure.

FIG. 9 depicts a flow diagram of an expected performance estimationmethod according to embodiments of the present disclosure.

DETAILED DESCRIPTION

A typical task assignment system assigns a finite number of tasks to afinite number of workers (“agents”) over a period of time. One exampleof a task assignment system is a contact center (e.g., a call center).In a call center, a finite number of agents are available during a givenshift or other period of time, and a finite number of callers call intothe call center during the shift. Each caller, with various needs andreasons for calling, represents a task assigned to one of the callcenter agents.

A typical task assignment strategy determines which tasks are assignedto which agents. Typically, a task assignment strategy is derived frominsights that certain types of agents perform better with certain typesof tasks, and these agents are assigned specific tasks based on theseinsights. In the example of a call center, the insight may be thatagents skilled at sales should be preferentially assigned to salesqueues of callers seeking to make a purchase, while agents skilled attechnical support should be preferentially assigned to technical supportqueues of callers seeking a solution to a technical problem.

Although typical task assignment strategies may be effective atimproving the performance of typical task assignment systems in someinstances, in other instances they may have no substantial impact onperformance at best or degrade performance at worst. Typically,instances under which typical task assignment strategies may beineffective are those that do not account for the comparative advantageof agents assigned to different types of tasks. A general description ofcomparative advantage may be found in, e.g., Cowen and Tabarrok, ModernPrinciples: Microeconomics, 2d ed. (2011) at pp. 16-19, which is herebyincorporated by reference herein.

In view of the foregoing, it may be understood that there is a need fora system that enables estimation of the expected performance ofdifferent task assignment strategies for the assignment of a finitenumber of tasks to a finite number of agents over a period of time in atask assignment system.

FIG. 1 shows a block diagram of a task assignment system 100 accordingto embodiments of the present disclosure. The description hereindescribes network elements, computers, and/or components of a system andmethod for estimating expected performance in a task assignment systemthat may include one or more modules. As used herein, the term “module”may be understood to refer to computing software, firmware, hardware,and/or various combinations thereof. Modules, however, are not to beinterpreted as software which is not implemented on hardware, firmware,or recorded on a non-transitory processor readable recordable storagemedium (i.e., modules are not software per se). It is noted that themodules are exemplary. The modules may be combined, integrated,separated, and/or duplicated to support various applications. Also, afunction described herein as being performed at a particular module maybe performed at one or more other modules and/or by one or more otherdevices instead of or in addition to the function performed at theparticular module. Further, the modules may be implemented acrossmultiple devices and/or other components local or remote to one another.Additionally, the modules may be moved from one device and added toanother device, and/or may be included in both devices.

As shown in FIG. 1, the task assignment system 100 may include a taskassignment module 110. The task assignment system 100 may include aswitch or other type of routing hardware and software for helping toassign tasks among various agents, including queuing or switchingcomponents or other Internet-, cloud-, or network-based hardware orsoftware solutions.

The task assignment module 110 may receive incoming tasks. In theexample of FIG. 1, the task assignment system 100 receives m tasks overa given period, tasks 130A-130 m. Each of the m tasks may be assigned toan agent of the task assignment system 100 for servicing or other typesof task processing. In the example of FIG. 1, n agents are availableduring the given period, agents 120A-120 n. m and n may be arbitrarilylarge finite integers greater than or equal to one. In a real-world taskassignment system, such as a contact center, there may be dozens,hundreds, etc. of agents logged into the contact center to interact withcontacts during a shift, and the contact center may receive dozens,hundreds, thousands, etc. of contacts (e.g., calls) during the shift.

In some environments, known as “L0” environments, one of the m tasks(e.g., task 130A) may be ready for assignment to an agent, and one ofthe n agents (e.g., agent 120A) may be ready to receive an assignedtask. In an L0 environment, there is no choice of task or agentavailable, and a task assignment strategy may assign task 130A to agent130A.

In other environments, known as “L1” environments, one of the m tasks(e.g., task 130A) may be ready for assignment to an agent, and multipleagents (e.g., agent 120A and 120B) may be ready to receive an assignedtask. In an L1 environment, there is a choice among multiple availableagents, and a task assignment strategy may assign task 130A to eitheragent 120A or 120B.

In yet other environments, known as “L2” environments, multiple tasks(e.g., tasks 130A and 130B) may be ready assignment to an agent, and oneof the n agents (e.g., agent 120A) may be ready to receive an assignedtask. In an L2 environment, there is a choice among multiple availabletasks, and a task assignment strategy may assign either task 130A or130B to agent 120A.

In still other environments, known as “L3” environments, multiple tasks(e.g., tasks 130A and 130B) may be ready assignment to an agent, andmultiple agents (e.g., agent 120A and 120B) may be ready to receive anassigned task. In an L3 environment, there is a choice among multipleavailable agents and tasks, and a task assignment strategy may pair offsome or all of the available tasks to some or all of the availableagents (e.g., in a sequence of assignments or a single batchassignment).

These environments L0-L3, and various transitions among them, aredescribed in detail for the contact center context in, e.g., U.S. patentapplication Ser. No. 15/395,469, which is hereby incorporated byreference herein.

In some embodiments, a task assignment strategy module 140 may becommunicatively coupled to and/or configured to operate in the taskassignment system 100. The task assignment strategy module 140 mayimplement one or more task assignment strategies (or “pairingstrategies”) for assigning individual tasks to individual agents (e.g.,pairing contacts with contact center agents).

A variety of different task assignment strategies may be devised andimplemented by the task assignment strategy module 140. In someembodiments, a first-in/first-out (“FIFO”) strategy may be implementedin which, for example, the longest-waiting agent receives the nextavailable task (in L1 environments) or the longest-waiting task isassigned to the next available task (in L2 environments). Other FIFO andFIFO-like strategies may make assignments without relying on informationspecific to individual tasks or individual agents.

In other embodiments, a performance-based routing (PBR) strategy may beused for prioritizing higher-performing agents for task assignment maybe implemented. Under PBR, for example, the highest-performing agentamong available agents receives the next available task. Other PBR andPBR-like strategies may make assignments using information aboutspecific agents but without necessarily relying on information aboutspecific tasks or agents.

In yet other embodiments, a behavioral pairing (BP) strategy may be usedfor optimally assigning tasks to agents using information about bothspecific tasks and specific agents. Various BP strategies may be used,such as a diagonal model BP strategy or a network flow BP strategy.These task assignment strategies and others are described in detail forthe contact center context in, e.g., U.S. Pat. No. 9,300,802 and U.S.patent application Ser. No. 15/582,223, which are hereby incorporated byreference herein.

In some embodiments, a historical assignment module 150 may becommunicatively coupled to and/or configured to operate in the taskassignment system 100 via other modules such as the task assignmentmodule 110 and/or the task assignment strategy module 140. Thehistorical assignment module 150 may be responsible for variousfunctions such as monitoring, storing, retrieving, and/or outputtinginformation about agent task assignments that have already been made.For example, the historical assignment module 150 may monitor the taskassignment module 110 to collect information about task assignments in agiven period. Each record of a historical task assignment may includeinformation such as an agent identifier, a task and/or task typeidentifier, and outcome information.

In some embodiments and for some contexts, additional information may bestored. For example, in a call center context, the historical assignmentmodule 150 may also store information about the time a call started, thetime a call ended, the phone number dialed, and the caller's phonenumber. For another example, in a dispatch center (e.g., “truck roll”)context, the historical assignment module 150 may also store informationabout the time a driver (i.e., field agent) departs from the dispatchcenter, the route recommended, the route taken, the estimated traveltime, the actual travel time, the amount of time spent at the customersite handling the customer's task, etc.

In some embodiments, the historical assignment module 150 may generate apairing model or similar computer processor-generate model based on aset of historical assignments for a period of time (e.g., the past week,the past month, the past year, etc.), which may be used by the taskassignment strategy module 140 to make task assignment recommendationsor instructions to the task assignment module 110. In other embodiments,the historical assignment module 150 may send historical assignmentinformation to another module such as the task assignment strategymodule 140 or the expected performance estimation module 160 to generatea pairing model and/or a pairing strategy based on a pairing model.

In some embodiments, an expected performance estimation module 160 maybe communicatively coupled to and/or configured to operate in the taskassignment system 100 via other modules such as the task assignmentmodule 110 and/or the historical assignment module 150. The expectedperformance estimation module 160 may estimate the expected performanceof a task assignment strategy (e.g., in conjunction with a pairingmodel) using historical assignment information, which may be receivedfrom, for example, the historical assignment module 150. The techniquesfor estimating expected performance and other functionality performed bythe expected performance estimation module 160 for various taskassignment strategies and various contexts are described in latersections throughout the present disclosure.

In some embodiments, the expected performance estimation module 160 mayoutput or otherwise report or use the estimated expected performance.The estimated expected performance may be used to assess the quality ofthe task assignment strategy to determine, for example, whether adifferent task assignment strategy (or a different pairing model) shouldbe used, or to predict the expected overall performance (or performancegain) that may be achieved within the task assignment system 100 when itis optimized or otherwise configured to use the task assignmentstrategy.

As noted above, a variety of contexts may use embodiments similar to thetask assignment system 100, including but not limited to contact centersand dispatch centers. One such example for contact centers is describedbelow with reference to FIG. 2.

FIG. 2 shows a block diagram of a contact center 200 according toembodiments of the present disclosure. Contact center 200 is similar tothe task assignment system 100 (FIG. 1) insofar as it is a specializedcontext for assigning tasks (namely, “contacts”) to agents in thecontact center. In an inbound environment, contacts call or otherwiseconnect to a switch or other component of the contact center 200 (via,e.g., live text chat, video chat, email, social media). In an outboundenvironment, contacts may call (or call back) or otherwise be connectedvia an outbound dialer or other component of the contact center 200 andcontemporaneously or subsequently assigned to an agent.

Similar to the task assignment system 100, contact center 200 has nagents 220A-220 n and m contacts 230A-230 m that arrive for assignmentto the agents over a given period. Switch 210 or a similar routingcomponent such as a PBX/ACD or load balancer may connect individualcontacts to individual agents.

Similar to task assignment strategy module 140, a contact pairingstrategy module 240 (e.g., a BP module and/or a benchmarking module) maymake pairing recommendations or instructions to the Switch 210 inaccordance with a contact pairing strategy.

Similar to historical assignment module 150, a historical contactpairing module 250 may monitor, store, retrieve, and/or outputinformation about agent contact pairings that have already been made.The historical contact pairing module 250 may generate a pairing model,which may be used by the contact pairing strategy module 240 to maketask assignment recommendations or instructions to the switch 210. Inother embodiments, the historical contact pairing module 250 may sendhistorical assignment information to another module such as the contactpairing strategy module 240 or the expected performance estimationmodule 160 to generate a pairing model for use with a pairing strategy.FIGS. 3A and 3B, described in detail below, depict examples of suchpairing models for simplified task assignment systems.

FIG. 3A depicts a schematic representation of a task assignment model300A according to embodiments of the present disclosure. The taskassignment model 300A models a simple task assignment system forillustrative purposes with three agents a₀-a₂ and three task typest₀-t₂. In some embodiments, agents and/or task types may be orderedaccording to some information about the agents or the task types (e.g.,a diagonal BP model). In other embodiments, the agents and task typesmay appear in the model without a particular ordering (e.g., a payoutmatrix or a network flow BP model).

In the task assignment model 300A, each cell represents a possibleassignment of a particular task type t_(i) with a particular agenta_(k). Each cell contains an interaction term (function) g(a_(k), t_(i))for the agent and task type. For example, an assignment of task type t₁to agent a₂ is shown to have an interaction term of g(a₂, t₁). Thespecific functional definition of any given interaction term depends onthe task assignment strategy to be used, the context for the taskassignment system, the data available for the given agent and task typeused to construct the task assignment model 300A, etc.

In some embodiments, the interaction term may represent a cost or valueof a particular pairing (e.g., expected conversion rate in a salesqueue, expected customer satisfaction rating in a customer supportqueue, expected cost of a truck roll in a dispatch center, etc.). Ineach case, the expected value may be estimated or otherwise determinedusing a combination of information about the agent and the type of task.

FIG. 3B depicts a schematic representation of a contact pairing model300B according to embodiments of the present disclosure. Like the taskassignment model 300A (FIG. 3A), the contact pairing model 300B models asimple contact center for illustrative purposes with three agents a₀-a₂and three contact types c₀-c₂, which may be the tasks in a contactcenter context. Each cell of the contact pairing model 300B indicatesthe value of the interaction term for each possible pairing ofindividual agents and contact types. The contact pairing model 300B maybe suitable for a diagonal BP strategy as described in, e.g., U.S. Pat.No. 9,300,802, which was previously incorporated by reference herein.

Consistent with a diagonal model, the preferred pairings fall along theequivalent of a “y=x” 45° diagonal line through the contact pairingmodel 300B, namely: a₀ with c₀, a₁ with c₁, and a₂ with c₂. Each ofthese cells found along the diagonal is shown to have an interactionterm that evaluates to 1.

In some situations, optimal choice of agents (L1) or contacts (L2) isnot always available to select the preferred agent for every contact(L1) or to select the preferred contact for every agent (L2). Insituations with limited choice, the pairing strategy may select thebest-available option. For example, the next best pairings as shown inthe contact pairing model 300B are in the cells relatively close to they=x diagonal. Each of these cells is shown to have an interaction termthat evaluates to 0.5. Moving farther still from the ideal diagonalpairs are the least-preferred pairs: a₀ with c₂ and a₂ with c₀, both ofwhich have interaction terms that evaluate to 0.

A pairing model such as contact pairing model 300B for a contact centeris one example context for a task assignment system. Other contextsmentioned above included a repair technician dispatched on a truck rollfrom a dispatch center, and a consulting associate tasked to a specificproject by her consulting firm. More examples of contexts include caseassignments (e.g., insurance claims) to agents (e.g., insurance claimadjusters), and recognizing retail customers for pairing with individualsalesclerks in a retail store. These contexts serve as example taskassignment systems, and embodiments of the present disclosure are notlimited to these contexts.

Unlike task assignment model 300A and contact pairing model 300B,typical work assignment strategies assign workers (or “agents”) to tasksbased on potentially naive intuitions. For example, in a contact center,tasks may be assigned to an agent based on agent performance (e.g.,PBR). Similarly, a repair technician may be assigned a truck routecalculated to minimize the length of the truck route. As anotherexample, a consulting firm might assign an associate to a specificproject based on the associate's tenure.

In all these cases, what is lacking is an assessment of the effect ofassignment of an individual worker to an individual task on theremainder of the workers and tasks within an overall system. Forexample, in a contact center environment, assignment of one task to ahigh-performing agent may necessitate assigning a different task to alow-performing agent, without due regard for the types of tasks beingassigned to high- and low-performing agents. In aggregate the entirecontact center's performance may be reduced. Similarly, assigning acertain route to a repair technician may result in assignments of otherroutes to other repair technicians such that the overall systemperformance may be reduced.

As a result, while an individual agent may indeed perform well with anassigned task, another agent assigned a residual task may performmaterially worse. Counterintuitively, attempting to optimize each taskassignment independently may, in fact, lower the overall performance ofthe task assignment system rather than increase it.

Embodiments of this disclosure provide techniques for more accuratelyestimating the performance of task assignment strategies. The techniquesassign tasks to agents in a manner that accounts for the cumulativeeffect of subsequent assignments over a period of time to optimizeoverall system performance rather than optimizing the performance if anyindividual assigned task. For example, the task assignment strategy mayleverage a comparative advantage of using some agents for some types oftasks while using other agents for other types of tasks.

FIGS. 4A-4K show schematic representations of expected performanceestimations for task assignment strategies, stepping through severaltechniques for estimating performance estimation. These examplesprimarily depict estimating expected performance of a diagonal model BPstrategy in a task assignment system under different conditions. Thetechniques use historical task assignment data to estimate expectedperformance and validate the strategy.

Specifically, as described in more detail below, FIGS. 4A-4C illustratea validation technique for estimating expected performance of a diagonalBP model using historical assignment data. FIGS. 4E and 4F accompany theexplanation below for a technique for improving the accuracy of theestimation technique described with reference to FIGS. 4A-4C when thereis an agent-selection bias in the underlying historical assignment data.FIGS. 4G and 4H accompany the explanation below for a technique forimproving the accuracy of the estimation technique described withreference to FIGS. 4A-C when there is a task-selection bias in theunderlying historical assignment data. FIGS. 4I and 4J accompany theexplanation below for a technique to compare the estimated expectedperformance of the task assignment strategy being validated to the taskassignment strategy that resulted in the underlying historicalassignment data. Finally, FIG. 4K accompanies the explanation below fora technique to visualize the distribution of freedom of choice found inthe underlying historical assignment data to improve the real-worldexpectations of an estimated expected performance of the task assignmentstrategy being validated.

FIG. 4A shows a schematic representation of a task assignment strategyexpected performance estimation 400A according to embodiments of thepresent disclosure. In this task assignment system, there may be anarbitrary finite number of agents and task types. Under the BP strategydiagonal model, each agent may be assigned an agent percentile rankingbetween 0 and 1, and each task type may be assigned a task percentileranking between 0 and 1. The ideal or optimal pairings, at which adiagonal BP strategy is expected to operate at peak performance withideal choice, are shown as a dashed diagonal line along y=x (i.e., theline along which Task Percentile equals Agent Percentile).

Historical assignment data may be received. In the schematicrepresentation of expected performance estimation 400A, each of thehistorical assignments is shown on a graph. Points indicated with theletter “O” represent pairings that had desirable outcomes, and pointsindicated with the letter “X” represent pairings that had undesirableoutcomes. For example, in a contact center sales queue, an “O” mayindicate a historical task in which a sale was made, and an “X” mayindicate a historical task in which a sale was not made (a binomialoutcome variable). In other examples, multinomial or continuous outcomevariables may be used.

If a task assignment system uses a FIFO pairing strategy or anotheressentially random or relatively uniformly distributed pairing strategy,a set of historical assignments may be relatively uniformly distributedthroughout a graph such as expected performance estimation 400A. Inother words, under FIFO, there is an equal probability that a task for agiven type may be assigned to any of the agents, with roughly equalutilization. Some historical assignments may appear close to thediagonal line (preferred pairings under the diagonal BP strategy), whileother historical assignments may appear farther from the diagonal line(non-preferred pairings), and so on.

In expected performance estimation 400A, the full set of 29 historicalassignments are shown. The set contains 12 pairings with desirableoutcomes (the O's) and 17 pairings with undesirable outcomes (the X's).In some embodiments, the estimated expected performance of the baselineor underlying task assignment strategy (e.g., FIFO as in this example)may be computed as the proportion of desirable outcomes found in theset: 12/2941%.

A diagonal BP strategy seeks to improve upon other pairing strategies bypreferentially pairing tasks to agents that are most similar inpercentile ranking, such that if these pairs were plotted on a chart,they would lie as close as possible to the y=x diagonal line (i.e., TaskPercentile=Agent Percentile).

In some embodiments, the expected performance of a task assignmentstrategy may be estimated (e.g., validated) using historical assignmentdata. In some embodiments, the validation may be performed using thesame historical assignments used to construct the pairing model. Inother embodiments, one set of historical assignments may be used toconstruct the pairing model, and a different set of historicalassignments may be used to validate the model.

An insight for validating a task assignment strategy with historicalassignment data is that the set of historical assignments can be sampled(or weighted, etc.) according to how likely it would have occurred hadthe task assignment system been running the pairing strategy beingvalidated instead of the underlying pairing strategy that produced thehistorical assignments.

In the case of a diagonal BP strategy, there is a convenient geometricrepresentation of a validation technique used in some embodiments andillustrated by FIGS. 4B and 4C. Namely, the closer a historical pairinglies to the ideal diagonal line, the more likely it is that such ahistorical pairing would have occurred using the diagonal BP strategybeing validated. A partition may be established for excluding historicalassignments from the sample that exceed a certain distance from thediagonal.

For a good diagonal pairing model, there should be proportionally moredesirable outcomes within the sample as the acceptable distance (athreshold distance, or threshold “closeness of fit”) for the sampleapproaches closer to the diagonal line. FIG. 4A shows the entirevalidation set of historical pairings, FIG. 4B shows a relatively largesample (relatively far acceptable/threshold distance from the diagonal),and FIG. 4C shows a relatively narrow sample (relatively shortacceptable/threshold distance from the diagonal).

FIG. 4B shows a schematic representation of a task assignment strategyexpected performance estimation 400B according to embodiments of thepresent disclosure. In expected performance estimation 400B, the plot ofhistorical tasks is shown again, except two regions beyond a specifieddistance from the diagonal have been grayed out. In expected performanceestimation 400B, the remaining sample contains 21 historicalassignments, including 10 pairings with desirable outcomes (the O's).Therefore, the estimated expected performance of the diagonal BPstrategy given this distance from the ideal, peak performance may bedetermined to be 10/21≈48%.

Comparing the expected performance of ≈48% to the underlying performanceof ≈41% shown with reference to expected performance estimation 400A(FIG. 4A), the expected improvement (or expected “gain”) provided bythis diagonal BP strategy over the underlying strategy may beapproximately 17%. This expected gain estimate assumes that the typicalamount of (limited) choice available in this task assignment systemtends to yield pairings distributed throughout this relatively wide bandof pairings.

FIG. 4C shows a schematic representation of a task assignment strategyexpected performance estimation 400C according to embodiments of thepresent disclosure. Expected performance estimation 400C depicts anarrower band of pairings (i.e., shorter acceptable distance from thediagonal to include in the sample) than expected performance estimation400B (FIG. 4B), and the excluded regions are larger. In expectedperformance estimation 400C, the subset of 12 historical assignmentscontained 8 pairings with desirable outcomes (the O's). Therefore, theestimated expected performance of the diagonal BP strategy may bedetermined to be 8/1267%, or an approximately 63% gain over theunderlying strategy for this amount of (less limited) choice, whichtends to yield pairings distributed throughout this relatively narrowband.

In the example of FIGS. 4A-4C, the expected performance increased as theband for sampling narrowed, an indicator that this diagonal BP model maybe effective for optimizing or otherwise increasing the performance ofthe task assignment system as compared to the underlying task assignmentstrategy (e.g., FIFO).

In some embodiments, arbitrarily many samples may be measured at varyingdistances from the diagonal, starting with the full set and ending withan infinitesimally small distance from the diagonal.

As the band narrows, approaching closer to an infinitesimally small bandaround the diagonal (representing peak performance with ideal, optimalchoice for every pairing), more and more historical tasks are excludedas being pairings that the diagonal BP strategy would likely not havemade (being too far from the preferred pairings closer to the diagonal).This effect is apparent in FIGS. 4A-4C: FIG. 4A included 29 historicalassignments (the full set), FIG. 4B sampled 21 of the historicalassignments, and FIG. 4C sampled only 12.

FIG. 4D shows a schematic representation of a task assignment strategyexpected performance estimation 400D according to embodiments of thepresent disclosure. Expected performance estimation 400D shows acorrelation curve when plotting out the expected performance (e.g.,ratio of desirable outcomes to sample size) against varying degrees ofthreshold closeness of fit. The correlation curve starts near top leftand drops off toward bottom right, indicating that a sample'sperformance increases as the threshold closeness of fit narrows towardthe preferred task assignment strategy (e.g., pairing tasks with agentsthat fall close to the diagonal).

In a real-world task assignment system using a BP task assignmentstrategy, actual task assignments may be found throughout the pairingspace, with many pairings relatively close to the optimal diagonal, andwith other pairings relatively far from the optimal diagonal. Thedistribution of assignments at varying degrees of threshold closeness offit can help estimate how well the BP task assignment strategy achievespeak performance. Comparing this distribution of real-world (e.g., BP“On” data) to the expected performance estimation 400D may allow for anincreasingly accurate estimate of overall expected performance. In someembodiments, the expected performance may be a simple average of theperformance of samples across varying degrees of closeness of fit. Inother embodiments, the expected performance may be a weighted average ofthe performance of samples across varying degrees of closeness of fitand weighted according to the distribution of pairings found incollections of “On” data when the task assignment system was using apreferred pairing strategy (e.g., a BP strategy). In other embodiments,other formulae may be applied to estimate the expected performance orgain in the task assignment system using the correlation curve ofexpected performance estimation 400D.

As more and more historical tasks are excluded from increasingly narrowsamples, the amount of data available to determine estimated gaindecreases, so the accuracy of the estimation decreases as well. Indeed,at some sufficiently narrow band, all of the historical assignment datamay be excluded, resulting in an empty sample with an undefined (“0/0”)expected performance.

Consequently, it may be beneficial in some embodiments to compute theexpected accuracy of the expected performance estimates (e.g., standarderror) for each band tested. In these embodiments, the accuracy or errorinformation would be available to help assess the reliability of a givenexpected performance estimation.

As above, in these embodiments, an arbitrarily large number ofestimations and accuracy/error measurements may be made stepping throughincreasingly narrow bands, excluding more and more historical tasks asthe band approaches closer and closer to optimal pairing until noneremain.

The example shown in FIGS. 4A-4C used a single set of historical data.In some embodiments, this validation process can be repeated forarbitrarily many different sets of historical data. In some embodiments,each of the one or more historical assignment sets may be a “holdoutset” or “validation set” that is wholly or at least partially differentfrom the “training set” used to create the pairing strategy. In otherembodiments, some or all of the historical assignment sets may be“in-samples” taken from a larger set of historical assignments used tocreate the pairing strategy.

In some embodiments, for either holdout sets or in-sample sets, thesesamples may be oversampled, counting a single historical assignmentmultiple times across multiple samples, for situations where suchoversampling techniques are useful for determining more accurateexpected performance estimations. For a simplistic example, if a holdoutset contains five historical assignments labeled A-E, the first samplemay contain historical assignments A, B, and C; the second sample maycontain historical assignments B, C, and D; the third sample may containhistorical assignments C, D, and E; and so on. In this example,historical assignment B is oversampled, included in at least the firstand second samples. In another example, such as when oversampling for anarrowing threshold closeness of fit, the first (largest) sample maycontain historical assignments A-E; the second (smaller) sample maycontain historical assignments B-D; and so on, to the smallest samplethat may contain only historical assignment B.

Embodiments of the present disclosure may use one or more of a varietyof different validation techniques, such as k-fold, random, time, randomtime, random rolling, off data, train on/off, train off, lift curve,etc. In some embodiments, the validation techniques may also includenormalization for time-based changes in the call center systemenvironment. Generalized k-fold validation techniques and some of theseother techniques are described in detail in, e.g., James et al., AnIntroduction to Statistical Learning (2013), at pp. 29-33 and 176-86,and Hastie et al., The Elements of Statistical Learning, 2d ed. (2008),at pp. 219-57, which are hereby incorporated by reference herein.

In the preceding example, the underlying task assignment strategy mayhave been FIFO, which resulted in historical assignments that weredistributed relatively uniformly throughout the space of possiblepairings. However, in some task assignment systems, a different taskassignment strategy may have been used that introduces utilization biasto the agents and/or tasks. FIGS. 4E and 4F show an example of agentutilization bias due to PBR, and FIGS. 4G and 4H show an example of taskutilization bias due to a task prioritization strategy (e.g.,prioritized or “VIP” call routing in a call center).

FIG. 4E shows a schematic representation of a task assignment strategyexpected performance estimation 400D according to embodiments of thepresent disclosure. In this example, most of the historical assignmentsare clustered toward the right side of the graph, around agents havinghigher percentile rankings. In this example, agent percentile isproportional to agent performance, and this agent utilization bias isdue to having used PBR as the underlying pairing strategy for thehistorical assignments. In other embodiments or contact centerenvironments, percentiles may correspond to metrics other thanperformance. For example, agent percentile may be proportional to eachagent's ability to influence the outcome of a call regardless of theagent's overall performance (e.g., amount of revenue generated).

Consequently, there is proportionally less data available for agents atlower percentiles. Thus, if left uncorrected, this bias could also skewor bias expected performance estimations as explained below withreference to FIG. 4F.

FIG. 4F shows a schematic representation of a task assignment strategyexpected performance estimation 400E according to embodiments of thepresent disclosure. Expected performance estimation 400E depicts thesame historic assignments as expected performance estimation 400D, withthe regions outside the band, farther from the diagonal, have beenexcluded.

The subset of included historic assignments also have a biaseddistribution, skewed toward higher-ranking agents. A naive approach toestimating expected performance for this band would note that there are9 desirable outcomes out of a total of 11 historic agent tasks. However,many of these desirable outcomes are clustered around higher-performingagents and so may lead to an unrealistically high expected performanceestimation.

Therefore, in some embodiments, expected performance may be estimatedmore accurately by weighting each vertical slice of historic assignmentsproportionally according to the number of historic assignments foundwithin a given slice. Reweighting the subset of historic assignments inthis way (i.e., “Agent Percentile Correction” or “AP Correction”) mayremove the bias from the underlying PBR strategy, yielding a moreaccurate estimate of expected performance.

FIG. 4G shows a schematic representation of a task assignment strategyexpected performance estimation 400F according to embodiments of thepresent disclosure. In this example, most of the historical assignmentsare clustered toward the top of the graph, around tasks having higherpercentile rankings. In this example, this task utilization bias is dueto having used a task prioritization strategy as the underlying pairingstrategy for the historical assignments.

Consequently, there is proportionally less data available for tasks atlower percentiles. Thus, if left uncorrected, this bias could also skewor bias expected performance estimations as explained below withreference to FIG. 4H.

FIG. 4H shows a schematic representation of a task assignment strategyexpected performance estimation 400G according to embodiments of thepresent disclosure. Expected performance estimation 400G depicts thesame historic assignments as expected performance estimation 400F, withthe regions outside the band, farther from the diagonal, have beenexcluded.

The subset of included historic assignments also have a biaseddistribution, skewed toward higher-ranking tasks. A naive approach toestimating expected performance for this band would note that there are9 desirable outcomes out of a total of 11 historic agent tasks. However,many of these desirable outcomes are clustered around higher-performingagents and so may lead to an unrealistically high expected performanceestimation.

Therefore, in some embodiments, expected performance may be estimatedmore accurately by weighting each horizontal slice of historicassignments proportionally according to the number of historicassignments found within a given slice. Reweighting the subset ofhistoric assignments in this way (i.e., “Task Percentile Correction” or“TP Correction”, or for a contact center context, “Contact PercentileCorrection” or “CP Correction”) may remove the bias from the underlyingtask/contact prioritization strategy, yielding a more accurate estimateof expected performance.

In some embodiments, it may be useful to measure how well (or howpoorly) the underlying task assignment strategy optimizes performancerelative to the task assignment strategy under validation. FIGS. 4I and4J depict an example of one such technique applied to a diagonal BPpairing strategies.

FIG. 4I shows a schematic representation of a task assignment strategyexpected performance estimation 400H according to embodiments of thepresent disclosure. The x-axis is labeled “Realization of PeakPerformance” and proceeds from “High” near the origin to “Low” on theright. For a diagonal BP model, high realization of peak performanceindicates sampling historical assignments relatively close to the ideal,optimal diagonal line, at which hypothetical peak performance may beachieved. Low realization of peak performance indicates samplinghistorical assignments in a wider band spread out farther from thediagonal.

The y-axis is labeled “Sample Size” and proceeds from 0 near the originto n (here, the size of the full set of n historical assignments) at thetop. For a diagonal BP model, the sample size shrinks as the band sizebecomes increasingly narrow. As the band size approaches peakperformance along the diagonal, the sample size eventually drops to 0.As the band size approaches low performance, the sample size eventuallyreaches n, encompassing the entire set of historical assignments.

If the underlying task assignment strategy had been FIFO, whereby thehistorical assignments may be relatively evenly distributed throughouteach band, it may often be the case that sample size decreasesproportionally to the square of the width of the band as the widthdecreases toward peak performance. As such, FIFO is a neutral strategythat represents a baseline performance level within the task assignmentsystem. In expected performance estimation 400H, the dashed curverepresents this baseline performance level for each sample size.

In this example, the solid curve “bows above” the dashed baselineperformance curve, such that the sample size increases rapidly forrelatively high realizations of peak performance (relatively narrowbands). In these environments, historical assignments may appear to beclustered proportionally closer to the diagonal. In these environments,the underlying strategy that generated the historical assignments mayalready be achieving a relatively high realization of peak performancewhen compared to the task assignment strategy being validated. Thus, theexpected gain over the underlying (incumbent) strategy may be relativelylow as compared to FIFO.

FIG. 4J shows a schematic representation of a task assignment strategyexpected performance estimation 400I according to embodiments of thepresent disclosure. The expected performance estimation 400I is similarto the expected performance estimation 400H (FIG. 4I), expect in thisexample, the curve “bows below” the dashed baseline performance curve,such that the sample size increases slowly for relatively highrealizations of peak performance (relatively narrow bands). In theseenvironments, historical assignments may appear to be clustered inregions proportionally farther from the diagonal. In these environments,the underlying strategy that generated the historical assignments may beperforming worse than FIFO, which may be mathematically equivalent to astrategy that performs worse than random. Thus, the expected gain overthe underlying (incumbent) strategy may be relatively high as comparedto FIFO.

In some embodiments, it may be useful to estimate or otherwise predictwhich band or range of bands most likely models the “real-world” taskassignment system. In the real-world task assignment system, the taskassignment system will experience varying degrees of possible choiceover time as the supply of available agents to meet the demand ofwaiting tasks constantly fluctuates. The real-world distribution ofchoice likely peaks somewhere between ideal, optimal choice (peakperformance) and completely constrained, limited choice (e.g., alwaysone-to-one, or “L0”).

FIG. 4K illustrates a technique to visualize the distribution of freedomof choice found in the underlying historical assignment data to improvethe real-world expectations of an estimated expected performance of thetask assignment strategy being validated.

FIG. 4K shows a schematic representation of a task assignment strategyexpected performance estimation 400J according to embodiments of thepresent disclosure. In these embodiments, information about thedistribution or frequency of varying degrees of choice may be associatedwith the historical assignment information, and a band or range of bandsmay be determined to model the real-world task assignment system moreclosely than other bands/samples. Having identified this band or rangeof bands, these embodiments may output the estimated expectedperformance and/or standard error for the identified band or range ofbands as being the most probable expected performance.

In some embodiments, a workforce recommendation may be made to increaseor decrease agent staffing to increase the average amount of choiceavailable to a pairing strategy for selecting agents or tasks,respectively. In some embodiments, a pairing strategy may delay pairingswhen the amount of choice available is considered too low, allowing timefor more tasks and/or agents to become ready for pairing.

The preceding examples primarily discussed diagonal BP strategies. Insome embodiments, an expected performance may be estimated for othertypes of BP strategies such as a network flow BP strategy.

FIG. 5 shows a schematic representation of a task assignment payoutmatrix 500 according to embodiments of the present disclosure. Similarto task assignment model 300A (FIG. 3A) and contact pairing model 300B(FIG. 3B), payout matrix 500 shows three agents a₀-a₂ and three tasktypes t₀-t₂. Each cell contains the value of an interaction termg(a_(t), t_(k)) for a given agent and task type assignment.

In this example, three preferred pairings have an expected value of 1and fall along the diagonal, and the other less-preferred pairings havean expected value of 0.5 or 0. Unlike the example of contact pairingmodel 300B (FIG. 3B), the expected values of pairings do notconsistently decrease as the pairings get farther from the diagonal. Forexample, the pairing of task t₁ to agent a₂ (expected value of 0) iscloser to the diagonal than the pairing of task t₂ to agent a₂ (expectedvalue of 0.5).

In some embodiments, a diagonal pairing strategy may still provideoutstanding performance improvements and balanced agent utilization evenfor environments such as the highly simplified illustrative example oftask assignment payout matrix 500. In other embodiments, a differentpairing strategy, such as a network flow (or linear programming)-basedBP strategy may provide greater performance optimization while stillachieving a desired balance of agent utilization, such as forenvironments analogous to task assignment payout matrix 500 for which noordering of agents and tasks provide a consistent increase in expectedvalues as pairings' distance to the diagonal gets shorter (i.e., thecloseness of fit gets closer). The task assignment payout matrix 500 maybe used in conjunction with a network flow BP strategy as described in,e.g., U.S. patent application Ser. No. 15/582,223, which was previouslyincorporated by reference herein.

As with a diagonal BP strategy, a network flow BP strategy may also bevalidated using historical assignment data. However, because there is nogeometric analogy for a network flow BP strategy like distance from thediagonal line in a diagonal BP strategy, these validation techniques arenot readily illustrated in figures as they were in FIGS. 4A-4H. In someembodiments, the historical assignments may be sampled (or oversampled)repeatedly at one or more approximations to the network flow BPstrategy's peak performance given ideal or optimal amount of choice. Forexample, historical assignment samples size 3 (or 4 or more) may bedetermined.

For example, a sample of historical assignments may include a preferredpairing of a₀ to t₂ with a desirable outcome, a non-preferred pairing ofa₁ to t₁ with a desirable outcome, and a non-preferred pairing of a₂ tot₀ with an undesirable outcome. The underlying performance of thissample may be determined as the proportion of desirable outcomes in thesample, or 2/3≈67%.

Given a choice of three as in sample size three, non-preferred pairingsaccording to network flow 500B may be excluded. Consequently, only onehistorical assignment, a₁ to t₁ with a desirable outcome, is in thesample, or 1/1=100%.

In these embodiments, the amount of data available in any one sample ishighly constrained (e.g., only 3 historical assignments) in contrastwith dozens or many thousands of historical assignments that may be findin the full set. Thus, it may be especially important to repeatedlysample the historical assignments to determine frequencies of preferredpairings and the weighted proportions of those that had desirableoutcomes.

As with the diagonal BP strategy, it may be useful to determine whetherthe underlying strategy is already partially optimized and/or to correctfor overrepresentation or bias of agents and/or tasks in the historicalassignment data.

Although the techniques vary in the details depending on the type oftask assignment strategy being created and validated (e.g., diagonal BPstrategy validation techniques compared with network flow BP strategyvalidation techniques), these techniques may involve sampling orweighting historical assignment data. In some embodiments, thesetechniques may involve repeated sampling, oversampling, bias correction,approximation toward peak performance or optimal choice, expectedperformance estimation, expected gain estimation (comparisons tounderlying historical performance), accuracy/error measurements,expected real-world gain estimation (e.g., comparisons to underlyingdistribution of available choice), etc. FIGS. 6A-9 depict flow diagramsfor various expected performance estimation methods described above.

FIG. 6A shows a flow diagram of an expected performance estimationmethod 600A according to embodiments of the present disclosure. At block610, expected performance estimation method 600A may begin.

At block 610, a plurality of historical assignments may be received. Insome embodiments, the plurality of historical assignments may bereceived from a historical assignment module such as historicalassignment module 150 (FIG. 1) or a historical contact pairing module250 (FIG. 2). In some embodiments, the plurality of historicalassignments may be an in-sample of the plurality of historicalassignments that were also used to build, generate, construct, train,refine, or otherwise determine a task assignment (pairing) model or taskassignment (pairing) strategy. In other embodiments, the plurality ofhistorical assignments be an out-sample (holdout set, validation set,etc.) that include historical assignments that were not used for modelbuilding. After receiving the plurality of historical assignments, theexpected performance estimation method 600A may proceed to block 620A.

At block 620A, a sample of the plurality of historical assignments basedon a strategy for pairing agents with tasks may be determined. In someembodiments, the sample may be determined by an expected performanceestimation module such as expected performance estimation module 160(FIGS. 1 and 2). In some embodiments, the sample may be determined byanalyzing the plurality of historical assignments, including historicalassignments in the sample that are sufficiently likely to have occurredusing the task assignment strategy and excluding historical assignmentsfrom the sample that are sufficiently unlikely to have occurred. Forexample, in the case of a diagonal BP strategy, including pairings thatfall within a band or specified distance from the diagonal line. Afterdetermining the sample of the plurality of historical assignments basedon the pairing strategy, expected performance estimation method 600A mayproceed to block 630A.

At block 630A, an expected performance of the pairing strategy based onthe sample may be determined. In some embodiments, the determination orestimation of expected performance may be computed as the proportion ofdesirable outcomes (e.g., positive outcomes for binomial variables, orsufficiently positive outcomes for multinomial or continuous variables)to the total number of historical pairings in the sample. In otherembodiments, the expected performance estimation may be corrected orotherwise adjusted to account for bias that may exist in the underlyinghistorical assignment data, such as overrepresentation of a subset ofagents (e.g., under PBR) or overrepresentation of a subset of task types(e.g., under a task prioritization strategy). In some embodiments, theexpected performance estimation may account for the frequencies at whichsome of the historical assignments may have been oversampled (e.g.,counted multiple times within the same sample in accordance with asample determination technique). After determining the expectedperformance of the pairing strategy, expected performance estimationmethod 600A may proceed to block 640.

At block 640, the determined or estimated expected performance may beoutputted. In some embodiments, expected performance estimation module160 may out the estimated expected performance to the task assignmentmodule 110 (FIG. 1), the switch 210 (FIG. 2), or another component ormodule within a task assignment system or otherwise communicativelycoupled to the task assignment system.

In some embodiments, after outputting the estimated expected performancedetermined at block 630, the expected performance estimation method 600Amay return to block 620 to determine a different sample. In otherembodiments, the expected performance estimation method 600A may returnto block 610 to receive a different plurality of historical assignments(e.g., a different in-sample or a different holdout set). In otherembodiments, the expected performance estimation method 600A may end.

FIG. 6B shows a flow diagram of an expected performance estimationmethod 600B according to embodiments of the present disclosure. Theexpected performance estimation method 600B is similar to the expectedperformance estimation method 600A except that historical assignmentsmay be weighted instead of being included or excluded in a sample.

The expected performance estimation method 600B may begin at block 610.At block 610, a plurality of historical assignments may be received asin expected performance estimation method 600A. After receiving theplurality of historical assignments, the expected performance estimationmethod 600B may proceed to block 620B.

At block 620B, a weighting of at least one of the plurality ofhistorical assignments based on a strategy for paring agents with tasksmay be determined. In some embodiments, a weighting may be assigned toall of the historical assignments received at block 610. In someembodiments, a weighting of zero may be assigned to some of thehistorical assignments. In these embodiments, a zero-weight may besimilar to excluding the historical pairing from a sample as in block620A (FIG. 6A) of the expected performance estimation method 600A. Insome embodiments, a weighting may indicate a likelihood that thehistorical assignment would have occurred under the pairing strategybeing validated. After determining a weighting of at least one of theplurality of historical assignments, the expected performance estimationmethod 600B may proceed to block 630B.

At block 630B, an expected performance of the strategy based on theweighting may be determined. For example, the expected performance maybe computed as a weighted average of the value associated with each ofthe weighted historical assignments. As in block 630A of the expectedperformance estimation method 600A, the expected performance estimationmay be adjusted in various embodiments and situations, such as tocorrect for bias in the underlying historical assignment data. Afterdetermining the expected performance, the expected performanceestimation method 600B may proceed to block 640.

At block 640, the expected performance may be outputted as in theexpected performance estimation method 600A. In various embodiments, theexpected performance estimation method 600B may return to block 610 fora next plurality of historical assignments, 620B for a next weightingdetermination, or the expected performance estimation method 600B mayend.

FIG. 7 depicts a flow diagram of an expected performance estimationmethod 700 according to embodiments of the present disclosure. Theexpected performance estimation method 700 may begin at block 710.

At block 710, a plurality of historical assignments may be received.After receiving the plurality of historical assignments, the expectedperformance estimation method 700 may proceed to block 720.

At block 720, the plurality of historical assignments may be partitionedinto a training subset and a validation subset (holdout subset,out-sample). After partitioning the plurality of historical assignments,the expected performance estimation method 700 may proceed to block 730.

At block 730, a pairing strategy may be generated based on the trainingsubset. For example, the historical assignments may be used to identifypatterns automatically within the task assignment system, and/or thehistorical assignments may be used to compute values/costs for a pairingmodel or payout matrix. After generating the pairing strategy, theexpected performance estimation method 700 may proceed to block 740.

At block 740, expected performance of the pairing strategy may bedetermined based on the validation subset. In some embodiments, theexpected performance may be determined using any of the validationtechniques described herein such as expected performance estimationmethods 600A and 600B (e.g., determining a sample or weightings of thevalidation set, respectively; determining expected performance based onthe sample or weightings, respectively; and, in some embodiments,repeatedly sampling or weighting the historical assignment data). Afterdetermining the expected performance of the pairing strategy, theexpected performance estimation method 700 may proceed to block 750.

At block 750, the expected performance may be outputted. Afteroutputting the expected performance, some embodiments may return toblock 720 to obtain a next validation set or to block 740 to determine anext expected performance based on the validation subset. In otherembodiments, the expected performance estimation method 700 may end.

FIG. 8 depicts a flow diagram of an expected performance estimationmethod 800 according to embodiments of the present disclosure. Theexpected performance estimation method 800 is similar to expectedperformance estimation method 700 (FIG. 7), except that it explicitlydescribes embodiments that may repeat some of the blocks for multiplevalidation sets. At block 810, the expected performance estimationmethod 800 may begin.

At block 810, a plurality of historical assignments may be received.After receiving the plurality of historical assignments, the expectedperformance estimation method 800 may proceed to block 820. At block820, the plurality of historical assignments may be partitioned into atraining subset and a validation subset. After partitioning theplurality of historical assignments, the expected performance estimationmethod 800 may proceed to block 830. At block 830, expected performanceof the pairing strategy may be determined based on the validation set.After determining the expected performance, the expected performanceestimation method 800 may proceed to block 840.

At block 840, a determination may be made as to whether to repeat partof the method for a next validation subset. If yes, the expectedperformance estimation method 800 may return to, for example, block 820to partition a next validation subset and/or a next training subset, andto block 830 to determine expected performance based on the nextvalidation subset. If no, the expected performance estimation method 800may proceed to block 850.

At block 850, the combined expected performances (e.g., an averageexpected performance or a weighted average expected performance) for atleast two of the plurality of validation subsets may be outputted. Afteroutputting the combined expected performances, the expected performanceestimation method 800 may end.

FIG. 9 depicts a flow diagram of an expected performance estimationmethod 900 according to embodiments of the present disclosure. Theexpected performance estimation method 900 is similar to the processdescribed with reference to FIGS. 4A-4H and 5A-5B, in which samples arerepeatedly determined for estimating expected performance at increasingapproximations of an ideal, peak strategy (e.g., progressively narrowbands for a diagonal BP strategy or progressively increasing samplesizes for a network flow BP strategy. At block 910, the expectedperformance estimation method 900 may begin.

At block 910, a plurality of historical assignments may be received.After receiving the plurality of historical assignments, the expectedperformance estimation method 900 may proceed to block 920.

At block 920, a sample of the plurality of historical assignments may bedetermined based on a degree of realization relative to peak performanceof a pairing strategy (e.g., a particular band size or distance from thediagonal for a diagonal BP strategy or a particular sample size for anetwork flow BP strategy). After determining a sample, the expectedperformance estimation method 900 may proceed to block 930.

At block 930, an expected performance of the pairing strategy may bedetermined based on the sample, using any of the previously describedtechniques. After determining the expected performance, the expectedperformance estimation method 900 may proceed to block 940.

At block 940, a decision may be made whether to repeat for a next degreeof realization. If yes, the expected performance estimation method 900may return to block 920 to determine a next sample based on a nextdegree of realization (e.g., a narrower band in a diagonal BP strategy,or a larger sample size in a network flow BP strategy), and proceed toblock 930 to determine another expected performance based on this nextsample and next degree of realization. If no, the expected performanceestimation method 900 may proceed to block 950.

At block 950, the expected performance based on the plurality of samplesand an expected degree of realization relative of peak performance maybe outputted. For example, a chart may be provided plotting theestimated expected performance along the y-axis for each degree ofrealization on the x-axis. In other embodiments, the expectedperformance estimates may be combined (e.g., an average or weightedaverage). In other embodiments, a determination of “real-world”realization of peak performance may be estimated, and the expectedperformance at the real-world degree of realization may be outputted.After outputting the expected performance, the expected performanceestimation method 900 may end.

At this point it should be noted that estimating expected performance ina task assignment system in accordance with the present disclosure asdescribed above may involve the processing of input data and thegeneration of output data to some extent. This input data processing andoutput data generation may be implemented in hardware or software. Forexample, specific electronic components may be employed in an expectedperformance estimation module or similar or related circuitry forimplementing the functions associated with estimating expectedperformance in a task assignment system in accordance with the presentdisclosure as described above. Alternatively, one or more processorsoperating in accordance with instructions may implement the functionsassociated with estimating expected performance in a task assignmentsystem in accordance with the present disclosure as described above. Ifsuch is the case, it is within the scope of the present disclosure thatsuch instructions may be stored on one or more non-transitory processorreadable storage media (e.g., a magnetic disk or other storage medium),or transmitted to one or more processors via one or more signalsembodied in one or more carrier waves.

The present disclosure is not to be limited in scope by the specificembodiments described herein. Indeed, other various embodiments of andmodifications to the present disclosure, in addition to those describedherein, will be apparent to those of ordinary skill in the art from theforegoing description and accompanying drawings. Thus, such otherembodiments and modifications are intended to fall within the scope ofthe present disclosure. Further, although the present disclosure hasbeen described herein in the context of at least one particularimplementation in at least one particular environment for at least oneparticular purpose, those of ordinary skill in the art will recognizethat its usefulness is not limited thereto and that the presentdisclosure may be beneficially implemented in any number of environmentsfor any number of purposes. Accordingly, the claims set forth belowshould be construed in view of the full breadth and spirit of thepresent disclosure as described herein.

The invention claimed is:
 1. A method for validating a preferred taskassignment strategy in a task assignment system comprising: receiving,by at least one computer processor communicatively to and configured toperform task assignment operations in the task assignment system, anaverage size of a task queue or an average number of available agentsfor agent-task pairing in the task assignment system; determining, bythe at least one computer processor, an expected average amount ofchoice for agent-task pairing in the task assignment system based on theaverage size of the task queue or the average number of availableagents; calculating, by the at least one computer processor, a firstestimated performance level of the task assignment system using thepreferred task assignment strategy based on the expected average amountof choice for agent-task pairing in the task assignment system,outputting, by the at least one computer processor, the calculated firstestimated performance level of the task assignment system; andestablishing, in a switch of the task assignment system, a connectionbetween a task and an agent based upon the preferred task assignmentstrategy and the calculated first estimated performance level of thetask assignment system.
 2. The method of claim 1, further comprising:calculating, by the at least one computer processor, a second estimatedperformance level of the task assignment system using the preferred taskassignment strategy based on an optimum amount of choice for agent-taskpairing in the task assignment system; and outputting, by the at leastone computer processor, a difference between the calculated first andsecond estimated performance levels of the task assignment system. 3.The method of claim 1, further comprising: recommending, by the at leastone computer processor, an agent workforce increase, wherein the agentworkforce increase is expected to increase an expected average number ofavailable agents to increase the expected average amount of choice foragent-task pairing in the task assignment system to increase the firstestimated performance level.
 4. The method of claim 1, furthercomprising: recommending, by the at least one computer processor, anagent workforce decrease, wherein the agent workforce decrease isexpected to increase the average size of the task queue to increase theexpected average amount of choice for agent-task pairing in the taskassignment system to increase the first estimated performance level. 5.The method of claim 1, further comprising: delaying, by the at least onecomputer processor, establishing connections among at least one waitingtask and at least one available agent, wherein the delaying is expectedto increase an actual amount: of choice for agent-task pairing in thetask assignment system to increase an actual performance level of thetask assignment system.
 6. The method of claim 1, further comprising:receiving, by the at least one computer processor, a first plurality ofhistorical agent-task assignments, wherein each of the first pluralityof historical agent-task assignments includes a historical size of thetask queue or a historical number of available agents at the time of theeach of the first plurality of historical agent-task assignments; andoutputting, by the at least one computer processor, a frequencydistribution of varying amounts of choice for agent-task pairing in thetask assignment system over time based on the historical size of thetask queue or the historical number of available agents of the each ofthe first plurality of historical agent-task assign en s.
 7. The methodof claim 1, wherein the preferred task assignment strategy is abehavioral pairing strategy.
 8. The method of claim 7, wherein thebehavioral pairing strategy is a diagonal model behavioral pairingstrategy or a network-flow behavioral pairing strategy.
 9. A system forvalidating a preferred task assignment strategy in a task assignmentsystem comprising: at least one computer processor communicativelycoupled to and configured to perform task assignment operations in thetask assignment system, wherein the at least one computer processor isfurther configured to: receive an average size of a task queue or anaverage number of available agents for agent-task pairing in the taskassignment system; determine an expected average amount of choice foragent-task pairing in the task assignment system based on the averagesize of the task queue or the average number of available agents;calculate a first estimated performance level f the task assignmentsystem using the preferred task assignment strategy based on theexpected average amount of choice for agent-task pairing in the taskassignment system; output the calculated first estimated performancelevel of the task assignment system; and establish a connection betweena task and an agent based upon the preferred task assignment strategyand the calculated first estimated performance level of the taskassignment system.
 10. The system of claim 9, wherein the at least onecomputer processor is further configured to: calculate a secondestimated performance level of the task assignment system using thepreferred task assignment strategy based on an optimum amount of choicefor agent-task pairing in the task assignment system; and output adifference between the calculated first and second estimated performancelevels of the task assignment system.
 11. The system of claim 9, whereinthe at east one computer processor is further configured to: recommendan agent workforce increase, wherein the agent workforce increase isexpected to increase an expected average number of available agents toincrease the expected average amount of choice for agent-task pairing inthe task assignment system to increase the first estimated performancelevel.
 12. The system of claim 9, wherein the at least one computerprocessor is further configured to: recommend an agent workforcedecrease, wherein the agent workforce decrease is expected to increasethe average size of the task queue to increase the expected averageamount of choice for agent-task pairing in the task assignment system toincrease the first estimated performance level.
 13. The system of claim9, wherein the at least one computer processor is further configured to:delay establishing connections among at least one waiting task and atleast one available agent, wherein the delaying is expected to increasean actual amount of choice for agent-task pairing in the task assignmentsystem to increase an actual performance level of the task assignmentsystem.
 14. The system of claim 9, wherein the at least one computerprocessor is further configured to: receive a first plurality ofhistorical agent task assignments, wherein each of the first pluralityof historical agent task assignments includes a historical size of thetask queue or a historical number of available agents at the time of theeach of the first plurality of historical agent-task assignments; andoutput a frequency distribution of varying amounts of choice foragent-task pairing in the task assignment system over time based on thehistorical size of the task queue or the historical number of availableagents of the each of the first plurality of historical agent-taskassignments.
 15. An article of manufacture for validating a preferredtask assignment strategy in a task assignment system comprising: anon-transitory processor readable medium; and instructions stored on themedium; wherein the instructions are configured to be readable from themedium by at least one computer processor communicatively coupled to andconfigured to perform task assignment operations in the task assignmentsystem and thereby cause the at least one computer processor to operateso as to: receive an average size of a task queue or an average numberof available agents for agent-task pairing in the task assignmentsystem; determine an expected average amount of choice for agent-taskpairing in the task assignment system based on the average size of thetask queue or the average number of available agents; calculate a firstestimated performance level of the task assignment system using thepreferred task assignment strategy based on the expected average amountof choice for agent-task pairing in the task assignment system; outputthe calculated first estimated performance level of the task assignmentsystem; and establish a connection between a task and an agent basedupon the preferred task assignment strategy and the calculated firstestimated performance level of the task assignment system.
 16. Thearticle of manufacture of claim 15, wherein the at least one computerprocessor is further configured to: calculate a second estimatedperformance level of the task assignment system using the preferred taskassignment strategy based on an optimum amount of choice for agent-taskpairing in the task assignment system; and output a difference betweenthe calculated first and second estimated performance levels of the taskassignment system.
 17. The article of manufacture of claim 15, whereinthe at least one computer processor is further configured to: recommendan agent workforce increase, wherein the agent workforce increase isexpected to increase an expected average number of available agents toincrease the expected average amount of choice for agent-task pairing inthe task assignment system to increase the first estimated performancelevel.
 18. The article of manufacture of claim 15, wherein the at leastone computer processor is further configured to: recommend an agentworkforce decrease, wherein the agent workforce decrease is expected toincrease the average size of the task queue to increase the expectedaverage amount of choice for agent-task pairing in the task assignmentsystem to increase the first estimated performance level.
 19. Thearticle of manufacture of claim 15, wherein the at least one computerprocessor is further configured to: delay establishing connections amongat least one waiting task and at least one available agent, wherein thedelaying is expected to increase an actual amount of choice foragent-task pairing in the task assignment system to increase an actualperformance level of the task assignment system.
 20. The article ofmanufacture of claim 15, wherein the at least one computer processor isfurther configured to: receive a first plurality of historicalagent-task assignments, wherein each of the first plurality ofhistorical agent-task assignments includes a historical size of the taskqueue or a historical number of available agents at the time of the eachof the first plurality of historical agent-task assignments; and outputa frequency distribution of varying amounts of choice for agent-taskpairing in the task assignment system over time based on the historicalsize of the task queue or the historical number of available agents ofthe each of the first plurality of historical agent-task assignments.